Variables, Expressions, and Equations

Here’s a sample activity that provides a context students love – candy! – and helps them understand how to define a variable, write expressions, and write and solve equations. Remind students to use the actions and relationships described in the story as a guide in choosing operations for the expressions and equations. Also encourage students to draw pictures and models to help them understand the scenarios.

Defining a variable

Distribute small packs of M&M. Skittle, or other candies. Discuss with the class whether they think there is the same number of candies in each pack (there should be IF the weight is uniform and IF the weight of each candy is the same, so assume for this activity that there is the same number in each bag). Then ask how many candies there are in one pack. Accept estimates, but agree that we can’t really know until we open the bag and count. Since the number of candies is an unknown quantity, have students use a variable to represent the quantity.

Writing Expressions

Have students work with a partner to answer the following questions, using the variable they have defined to represent the number of candies in each pack.

1) How many candies are in 3 packs? In 5 packs? All together for the whole class?

2) How many candies will you have if I give you one pack and then 6 more candies?

3) How many candies will you have if you open your pack and share 2 candies with me?

4) How many candies will you have if you have 4 packs and I give you 7 more candies?

5) How many candies will you have if you have 3 packs and you give away 2 candies to a friend?

6) How many candies will you have if you have 5 packs, open them all, and give away 2 candies from each pack to friends?

7) Suppose you have one pack of candy. How many candies will you have if you open the pack and share the candies equally with 3 other friends?

8) Suppose you have 2 packs of candies. How many candies will you have if you open the packs and share the candies equally with 3 other friends?

9) If you have three packs and your friend has 5 packs, how many more candies does your friend have than you?

10) Suppose you have one pack of candy. If your friend has 6 more than twice as many candies as you have, how many candies does your friend have?

11) Suppose you have one pack of candy. If your friend has 4 less than 3 times as many candies as you have, how many candies does your friend have?

12) Suppose your friend has 100 candies and you have one pack of candies. How many more candies does your friend have than you?

13) Suppose your friend has 100 candies. You have one pack plus 6 more candies. How many more candies does your friend have than you?

14) Suppose your friend has 100 candies. You have one pack, which you open and share equally with another friend. How many more candies does your friend have than you?

Writing Equations

Next have students write and solve equations that represent the situations described below:

1) You have one pack of candies. You open it and count 14 candies. How many candies were in the pack?

2) You have one pack of candies. You open it but forget to count how many there are before eating 5 candies. Then you count and have 11 candies left. How many candies were in the pack?

3) You have one pack of candies and I give you 5 more candies. Then you open your pack, count all of your candies, and discover that you have 13 candies. How many candies were in the pack?

4) You have one pack of candies. You open it and share 4 candies with friends, and have 9 candies left. How many candies were in the pack?

5) You have one pack of candies. You open it and share the candies equally with 4 other friends. You get 5 candies. How many candies were in the pack?

6) You have three packs of candies. You open them and count 51 candies. How many candies were in each pack?

7) You have three packs of candies. You open them and share the candies equally with a friend. You get 18 candies. How many candies were in each pack?

8) You have three packs of candies. You pour them out and share 16 candies with friends. Then you count and see that you have 26 candies left. How many candies were in each pack?

9) You have three packs of candies. I give you 7 more candies. You open the packs and count all of your candies and see that you have 55 candies. How many were in each pack?

10) You have three packs of candies. I give you two more packs, but ask you to give me 6 candies. After opening one pack and giving me the candies, you open all your packs and count 44 candies. How many candies were in each pack?

Finally, as a culminating activity, have students describe situations for their partner to model, write equations, and solve in as many ways as they can. Create posters for the classroom with these problems and eat the candies, reminding students that algebra is both fun and sweet!